From my reading and limited
experience, no question about cuttings can be answered without reference to specific tree species, and even then answers are variable due to the wide-ranging diversity of tree genetics.
Trees range all the way from "sometimes a skilled nurseryman with an automated misting tank can get one cutting in 300 to take
root under lab conditions" to "I cut a six-foot chunk for
firewood in January and then in March I drove it into the ground small-end-first and tethered my goat to it, but now in August it is a twelve-foot tall tree." In other words, the dreaded
permaculture "it depends".
That said, when my trees take damage I often try to root the cuttings. My dogs ate a branch off my Wolf River
apple tree last summer, and (in high summer) I turned that into four cuttings that I stuck in a pot. This spring, one of those cuttings has leaves, although given how hard apples are to root, I still suspect it's a last-gasp effort stealing nutrients from the
cutting wood and probably doesn't have
roots. On the other hand I cut a bunch of elderberry cuttings from a fruiting stand last summer that was about to be sprayed by the power crew, and they not only took root right away and flowered in my pots before fall, they all seem to have survived the winter.
Thus my real
answer to your question is that the "proper" time to take cuttings is just a rule of thumb. It's the time when the consensus of experience agrees your cuttings are most likely to take root. So when the time is not "proper" but you have the cutting materials, what's the downside? Your time and propagation space, that's all. If you have
enough of those, I see no reason not to do it.